The pivotal idea of immersed finite element methods is to embed a complex geometry into a geometrically simple ambient domain, on which a regular mesh can be built easily. Basis functions defined on this ambient-domain mesh are then restricted to the problem geometry, after which the solution is approximated by a linear combination of these restricted basis functions. Although this discretization is conceptually straightforward, non-standard treatment of various aspects (which are discussed below) is required on account of the fact that the mesh does not fit the boundaries of the geometry.
Using a wide variety of techniques to treat these non-standard aspects, the concept of immersed finite element methods has successfully been applied in a broad range of fields, such as solid mechanics [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}; shell analysis [10]}, [8]}, [12]}, [9]}, [14]}, [15]}, [16]}; interface problems [17]}, [18]}, [19]}, [20]}, [21]}; fluid mechanics [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}; fluid-structure interaction [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, in particular fluid-structure interaction for biomedical applications [41]}, [42]}, [43]}, [44]}; scan-based analysis of both man-made and biological materials [45]}, [46]}, [47]}, [48]}, [49]}, [50]}, [51]}, [52]}, [53]}; shape and topology optimization [54]}, [55]}, [56]}, [57]}, [58]}, [59]}, [60]}; and many more.
<FIGURE>